Complementary decompositions of monomial ideals and involutive bases

Autor:	Hashemi, Amir, Orth, Matthias, Seiler, Werner M.
Rok vydání:	2022
Předmět:	Combinatorial decompositions Algebra and Number Theory Zerlegung Monomial ideals Applied Mathematics Involutive bases Primary decompositions Monomiales Ideal Quasi-stable ideals Kommutative Algebra
Zdroj:	Applicable Algebra in Engineering, Communication and Computing. 33:791-821
ISSN:	1432-0622 0938-1279
DOI:	10.1007/s00200-022-00569-0
Popis:	Complementary decompositions of monomial ideals—also known as Stanley decompositions—play an important role in many places in commutative algebra. In this article, we discuss and compare several algorithms for their computation. This includes a classical recursive one, an algorithm already proposed by Janet and a construction proposed by Hironaka in his work on idealistic exponents. We relate Janet’s algorithm to the Janet tree of the Janet basis and extend this idea to Janet-like bases to obtain an optimised algorithm. We show that Hironaka’s construction terminates, if and only if the monomial ideal is quasi-stable. Furthermore, we show that in this case the algorithm of Janet determines the same decomposition more efficiently. Finally, we briefly discuss how these results can be used for the computation of primary and irreducible decompositions.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2b58840b5a032dcf50d3c8811d027b54 https://doi.org/10.1007/s00200-022-00569-0 Zobrazit plný text záznamu Full text from SpringerLink